Theorems · Theorem · general algebraic systems
Finsupp.mem_support_iff
∀ {α : Type u_1} {M : Type u_4} [inst : Zero M] {f : α →₀ M} {a : α}, a ∈ f.support ↔ f a ≠ 0- Defined in
- Mathlib.Data.Finsupp.Defs
- Cited by
- 89 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Zero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Finsetstatement · cited by 13,712
- Finsuppstatement and proof · cited by 5,255
- Finsupp.supportstatement · cited by 828
- Finsupp.mem_support_toFunproof · cited by 2
Cited by89
Results whose statement or proof uses this declaration.
- Finsupp.notMem_support_iffproof · cited by 44
- Finsupp.sum_eq_singleproof · cited by 18
- Finsupp.inductionproof · cited by 12
- AddMonoidAlgebra.leadingCoeff_eq_zeroproof · cited by 9
- MvPolynomial.totalDegree_eq_zero_iff_eq_Cproof · cited by 9
- Finsupp.support_sumproof · cited by 7
- Finsupp.induction_on_maxproof · cited by 6
- Finsupp.support_indicator_subsetproof · cited by 5
- Finsupp.fun_support_eqproof · cited by 5
- Matrix.PosDef.diagonalproof · cited by 4
- MvPolynomial.IsHomogeneous.eval₂proof · cited by 3
- AddMonoidAlgebra.coeff_eq_zero_of_not_le_supDegreeproof · cited by 3